3-d localization error analysis in wireless networks

In the paper we investigate 3-D positioning by making use of distance/range and angle-of-arrival (AOA) measurements. Two estimation methods (linear least squares (LS) estimator and optimization) are developed for node positioning in wireless networks. We derive the Cramer-Rao lower bound (CRLB) for positioning with both range and AOA measurements in a 3-D environment, which is not seen in the literature. Also we derive compact approximate expressions of the variances of the LS algorithms. In the literature, positioning accuracy is usually studied by assuming perfect anchor location information. To evaluate positioning accuracy under realistic conditions, we also analyze the impact of anchor position error. Numerical results demonstrate that the derived analytical results have a good match with the simulated results.